Inverse numerical prediction of the transport properties of vertebral endplates in low back pain patients

Abstract

A numerical method based on contrast-enhanced MRI to predict the transport properties of spinal structures is presented and used for a population of 32 low back pain patients. Sixty-eight one-dimensional finite element models aimed to replicate the transport of Gd-HP-DO3A were developed, one for each intervertebral disc was investigated. Each model had the same disc height as that measured on the MRI images of specific patients. Transport properties of the vertebral structures were inversely calculated in order to minimize the error between the predicted Gd-HP-DO3A concentration and those determined by MRI acquisitions for specific patients 6 h after a contrast agent injection. Within some limits numerical predictions were generally representative of the Gd-HP-DO3A concentration behavior estimated by contrast-enhanced MRIs. The predicted properties showed high variability within the population. Transport properties were markedly higher than the bulk diffusion coefficients of the nutrients. No significant differences (p=0.31) were observed between the caudal and the cranial endplate zones. Discs had higher transport properties than endplate zones (p<0.001). Comparisons among different age groups revealed no significant differences of the transport properties with aging. The discrepancies between the predictions and the bulk diffusion coefficients of nutrients and Gd-HP-DO3A in water highlighted the complexities of quantifying transport across the EPZs and intervertebral disc.